Physics of Black and White Film
Conventional black and white film is comprised of silver-based light sensitive emulsion layers which undergoe chemical change in their light transmission properties upon exposure to light, and are subsequently developed. The silver emulsions used in films such as motion picture films are known to respond non-uniformly to differing colors of light, and to differing intensities and contrasts. Furthermore, the emulsions' response curves differ substantially from that of the human eye.
The degree to which a particular emulsion darkens in response to a given scene is primarily dependent on the overall intensity of light and the time of exposure. Commonly, intensity is controlled by an iris in the camera and is measured in F-stops. Time of exposure is controlled by a shutter and is measured in fractions of a second of exposure time.
A secondary determinant of the degree of darkness is the color of the light which is being used to expose the film. Since the silver emulsion of the film responds most strongly to only one particular wavelength, lights of equal intensity but differing color will produce differing darkness on the film, in direct relation to their closeness to the wavelength of maximum sensitivity of the film. For this reason, many photographers use colored filters (red or yellow, for instance) when using black and white film.
In photographing "real world" scenes, the amount of incident light, its source, its color, and the color of the objects comprising the scene are widely varied. For each unique combination of these factors, plus the additional filtering done by the photographer, the film produces a shade of gray. Because of the complex interactions of film response, colors, and shadings, however, these grays are not unique for each combination of these factors, and several combinations may produce the same shade of gray on film. For instance, a blue object photographed in bright light and a green one in dimmer light may appear identical in the black and white image. For this reason, early film directors used colors in sets and costumes which could be differentiated in the final film, often intentionally disregarding the actual appearance of the colors.
In strictly mathematical terms, the image produced on black and white film is one dimensional (brightness), while the original scene can be viewed as three dimensional (using the HLS model of color, where hue, luminance, and saturation are the dimensions). The chemical reaction of the film emulsion, and the camera mechanisms and filters essentially reduce the three dimensional information to one dimension by a complex mapping, and forever obliterate the original hue, luminance, and saturation information.
Note: It should be pointed out that luminance and brightness are not the same. Since brightness of the black and white image results from the complex interactions of the three elements of the HLS system, there is only a statistical correlation between brightness and luminance, but they are not identical.